Under the Foreign Sovereign Immunities Act (FSIA) 28 USC 1605, subsections (b-d) are clearly irrelevant (mortgage foreclosure, maritime liens). Under (a), the exception to immunity can be because of (1) waiver, (3-4) property takings in violation of international law and other property issues, and (6) contract enforcement. Then there are two more potentially applicable subsections. First there is
(2) in which the action is based upon a commercial activity carried on
in the United States by the foreign state; or upon an act performed in
the United States in connection with a commercial activity of the
foreign state elsewhere; or upon an act outside the territory of the
United States in connection with a commercial activity of the foreign
state elsewhere and that act causes a direct effect in the United
It would be a stretch to apply this exception, but the law is full of stretches. Then there is:
(5) not otherwise encompassed in paragraph (2) above, in which money
damages are sought against a foreign state for personal injury or
death, or damage to or loss of property, occurring in the United
States and caused by the tortious act or omission of that foreign
state or of any official or employee of that foreign state while
acting within the scope of his office or employment; except this
paragraph shall not apply to— (A) any claim based upon the exercise or
performance or the failure to exercise or perform a discretionary
function regardless of whether the discretion be abused, or (B) any
claim arising out of malicious prosecution, abuse of process, libel,
slander, misrepresentation, deceit, or interference with contract
There is a piece of congressional legal research suggesting that FSIA would not allow the suit, specifically looking at the Missouri suit against China. Missouri does indeed invoke (2) and (5). The analysis points out that there may be some connection between commercial activities and harm in the US, but that the harm is not "based directly on" such commercial activities. For example, operating a healthcare system in China does not directly cause damage in the US, nor does producing medical equipment, nor operating social media platforms (these are three of the claims of Missouri). Nor does conducting "commercial research on viruses by the Wuhan Institute and Chinese Academy of Sciences." SCOTUS explained in Argentina v. Weltover that the damage in the US must follow "as an immediate consequence" of the activity, not just an eventual result.
The main problem with the territorial tort claim in (5) is that the tort would appear to be a failure to perform a discretionary function in "allowing the virus to spread," but that reduces to saying that they failed to take sufficiently strenuous action to prevent the spread, and perhaps suppressing information. But the governments have discretion in these matters.
So under existing law, it is more likely than not that the courts would not apply an exception to the jurisdiction question.